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Earlier this year, I listened to Susan Rice, White House National Security Adviser, address the Women in the World conference in New York. Unsurprisingly, there was discussion aplenty about North Korea and the Middle East. But there was also abashed laughter about basketball. For before Rice embarked on a political career, she was a keen basketball player, playing point guard; indeed she was so obsessed with the game that she was apparently nicknamed “Spo”, short for “Sportin”. “I loved it!” she declared.

Just a coincidence? Perhaps not. In recent months Ernst & Young, the American consultancy, has been analysing sporting activity among senior female executives and leaders. And it has discovered that the higher the executive level, the more likely it is that a woman played sport at high school or college. Most notably, some 19 out of 20 women who sit in the “C-suite” – holding the title “chief something” – were sporty as a teenager; indeed, seven out of 10 still play sport as a working adult, while six out of 10 played sport at university. One in eight C-suite executives played sport professionally. However, among the middle levels of working women, athletic skill was lower: just a third of mid-level women, for example, played sport at university.

Now, this survey is – admittedly – based on a small sample size (there are simply not that many C-suite women around, compared with C-suite men). And there is no comparable data for stay-at-home mums, say. Nevertheless, the statistics echo a pattern that I have noticed in my own conversations with powerful women.

Sportiness seems so widespread among women such as Rice that it is actually hard to think of any executive who admits to having been a couch potato as a child. Think, for example, of IMF head Christine Lagarde (a former member of France’s synchronised swimming team), Condoleezza Rice (a keen figure skater in her youth) and Hillary Clinton (school baseball). Or Dilma Rousseff (the Brazilian president, who played volleyball to a high level), Indra Nooyi (the CEO of PepsiCo was a keen cricket player), Ellen Kullman (CEO at Dupont, who played basketball to a high level at college). Even Sheryl Sandberg, COO of Facebook, was formerly an aerobics instructor. And those are just examples that spring to mind.

Why? A cynic might suggest that this reflects the pressure on today’s elite – of either sex – to stay slim and healthy. You need stamina to climb that corporate ladder. Having a sense of teamwork and discipline also instils skills that are useful in the workplace, for women as much as men. Or as Beth Brooke, vice-chair of Ernst & Young says: “Not only do the majority of senior women executives have sports in their background, they recognise that the behaviours and techniques learned through sports are critical to motivating teams and improving performance in a corporate environment.”

I suspect, however, that there is something else more important – and subtle – going on too. Girls who play sport at school learn at a young age that it is acceptable to compete aggressively. They also discover that success does not depend on looking good and that it can be acceptable to take pleasure in winning. That might seem an obvious point, at least to an adult man. But it is not so self-evident to young girls who are exposed to modern Hollywood teen – or tweenie – culture. Indeed, when I look at the cultural messages that kids receive now from films and television, compared with my own childhood, I suspect that girls need sports today more than ever. Being an athlete is one of the few socially accepted ways for teenage girls to compete, without peer criticism.

This has at least two implications. First, it may suggest that if we want to find more future female business and civic leaders, we should look more closely at athletes. Historically, professional women athletes tend to be steered to coaching or commentators’ jobs when their sporting careers dim. However, Brooke of E&Y is now trying to create a network to turn more of them into entrepreneurs, and it will be interesting to see if this produces any results.

But second – and most obviously – we need to keep young girls playing sport. In my case, I was lucky enough to grow up competing extensively (lacrosse and netball were my passion). I am now trying to ensure that my own daughters do so too. However, this is a luxury of sorts. As public educational budgets get squeezed – and cyber distractions grow – it is becoming harder, not easier, for many girls to do team sports. That is a tragedy. If we want to get more strong female leaders, we must celebrate competition at a young age. Or, at least, teach them the links between struggle and success; even – or especially – in an age of instant gratification where kids prefer to say “don’t sweat it”.